For all proofs, a set of axioms is required to draw justified conclusions. For natural numbers, this framework is called the Peano Axioms:

1. 0 is a natural number.2. For every natural number x, x = x. 3. For all natural numbers x and y, if x = y, then y = x. 4. For all natural numbers x, y and z, if x = y and y = z, then x = z. 5. For all a and b, if a is a natural number and a = b, then b is also a natural number. 6. For every natural number n, S(n) is a natural number.7. For every natural number n, S(n) = 0 is false. 8. For all natural numbers m and n, if S(m) = S(n), then m = n.9. If K is a set such that: 0 is in K, and for every natural number n, if n is in K, then S(n) is in K, then K contains every natural number.

In this system, the numbers 1 and 2 are symbols, whose arithmetic form is: S(0) and S(S(0)).

To both PBJS and voters, I would like to point out to those without much mathematical knowledge that a "Binomial Base" is not an actual concept. In fact, the only correlation that 1 + 1 has with Binomials is its expression in the Binomial Theorem. To rewrite 1 + 1,

Reasons for voting decision: The resolution was "1+1 is 2"
Pro showed that 1+1 is, in fact, 2.
Con showed that 1+1 could be 10, but not that it isn't 2.
Next time, let's make it more rounds. Clash is the purpose of debate, rather than stating your opinion and hoping more people favor it than your opponent's.

Reasons for voting decision: Neither side distinguished their argument as better than the other. Pro would have probably won by default, if he had actually refuted anything at all (as opposed to just ignoring it).

You are not eligible to vote on this debate

This debate has been configured to only allow voters who meet the requirements set by the debaters. This debate either has an Elo score requirement or is to be voted on by a select panel of judges.